Orthogonal invariants of skew-symmetric matrices

Abstract

The algebra of invariants of d-tuples of n × n skew-symmetric matrices under the action of the orthogonal group by simultaneous conjugation is considered over an infinite field of characteristic different from two. For n = 3 and d > 0 a minimal set of generators is established. A homogeneous system of parameters (i.e. an algebraically independent set such that the algebra of invariants is a finitely generated free module over subalgebra generated by this set) is described for n = 3 and d > 0, for n = 4 and d = 2, 3, for n = 5 and d = 2.

Keywords:

• invariant theory
• classical linear groups
• generators
• homogeneous systems of parameters

AMS Subject Classifications:

• 16R30
• 15B10
• 13A50

Acknowledgements

The first version of this article was written during the author's visit to the University of Bielefeld, sponsored by DFG. The author is grateful for this support. This research was also supported by RFFI 10-01-00383a.